Splash Screen. Five-Minute Check (over Lesson 13–2) CCSS Then/Now New Vocabulary Key Concept: Length Probability Ratio Example 1: Use Lengths to Find Geometric Probability Example 2: Real-World Example: Model Real-World Probabilities Key Concept: Area Probability Ratio
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Key Concept: Length Probability Ratio
Example 1: Use Lengths to Find Geometric Probability
Example 2: Real-World Example: Model Real-World Probabilities
Key Concept: Area Probability Ratio
Example 3: Real-World Example: Use Area to Find Geometric Probability
Example 4: Use Angle Measures to Find Geometric ProbabilityLesson Menu
Answer:The probability that Z is on AB is , approximately 0.18, or approximately 18%.
Use Lengths to Find Geometric Probability
Length probability ratio
We can use a number line to model this situation. Since the comet orbits every 76 years, it will orbit again in 76 years or less. On the number line below, the event of an orbit in the next 10 years is modeled by EF.
Model Real-World Probabilities
ORBITS Halley’s Comet orbits the earth every 76 years. What is the probability that Halley’s Comet will complete an orbit within the next decade?Example 2
DARTS The targets of a dartboard are formed by 3 concentric circles. If the diameter of the center circle is 4 inches and the circles are spread 3 inches apart, what is the probability that a player will throw a dart into the center circle?
You need to find the ratio of the area of the center circle to the area of the entire dartboard. The radius of the center circle is 4 ÷ 2 or 2 inches, while the radius of the dartboard is 2 + 3 + 3 or 8 inches.Example 3
Answer:The probability that the dart hits in the center circle is or about 6%.
Use Area to Find Geometric Probability
Area probability ratio
A = πr2
RING TOSS If at a carnival, you toss a ring and it lands in the red circle shown below, then you win a prize. The diameter of the circle is 4 feet. If the dimensions of the blue table are 8 feet by 5 feet, what is the probability if the ring is thrown at random that you will win a prize?
A. about 31%
B. about 33%
C. about 35%
D. about 37%Example 3
A. about 17%
B. about 16%
C. about 18%
D. about 27%Example 4
A. about 24%
B. about 26%
C. about 27%
D. about 38%Example 4